NED Abstract

Copyright by American Astronomical Society.
Reproduced by permission
2002ApJ...574..740T
The Slope of the Black Hole Mass versus Velocity Dispersion Correlation
Scott Tremaine, Karl Gebhardt, Ralf Bender, Gary Bower, Alan Dressler,
S. M. Faber, Alexei V. Filippenko, Richard Green, Carl Grillmair,
Luis C. Ho, John Kormendy, Tod R. Lauer, John Magorrian, Jason Pinkney, and
Douglas Richstone
Received 2002 January 17; accepted 2002 April 3
ABSTRACT
Observations of nearby galaxies reveal a strong correlation between the
mass of the central dark object M_BH_ and the velocity dispersion
{sigma} of the host galaxy, of the form
log(M_BH_/M_sun_) = {alpha} + {beta}log({sigma}/{sigma}_0_); however,
published estimates of the slope {beta} span a wide range (3.75-5.3).
Merritt & Ferrarese have argued that low slopes (<~4) arise because of
neglect of random measurement errors in the dispersions and an incorrect
choice for the dispersion of the Milky Way Galaxy. We show that these
explanations and several others account for at most a small part of the
slope range. Instead, the range of slopes arises mostly because of
systematic differences in the velocity dispersions used by different groups
for the same galaxies. The origin of these differences remains unclear, but
we suggest that one significant component of the difference results from
Ferrarese & Merritt's extrapolation of central velocity dispersions to
r_e_/8 (r_e_ is the effective radius) using an empirical formula. Another
component may arise from dispersion-dependent systematic errors in the
measurements. A new determination of the slope using 31 galaxies yields
{beta} = 4.02 +/- 0.32, {alpha} = 8.13 +/- 0.06 for
{sigma}_0_ = 200 km s^-1^. The M_BH_-{sigma} relation has an intrinsic
dispersion in log M_BH_ that is no larger than 0.25-0.3 dex and may be
smaller if observational errors have been underestimated. In an appendix,
we present a simple kinematic model for the velocity-dispersion profile of
the Galactic bulge.
Subject headings: black hole physics - galaxies: bulges - galaxies:
fundamental parameters - galaxies: nuclei - Galaxy: bulge - Galaxy:
kinematics and dynamics